Random graphs of Internet type and the generalised allocation scheme
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Yu. L. Pavlov
Abstract
In order to simulate complex telecommunication networks, in particular, the Internet, random graphs are frequently used which contain N vertices whose degrees are independent random variables distributed by the law
P{η ≥ k} = k–τ,
where η is the vertex degree, τ > 0, k = 1, 2, …, and the graphs with identical degrees of all vertices are equiprobable. In this paper we consider the set of these graphs under the condition that the sum of degrees is equal to n. We show that the generalised scheme of allocating particles into cells can be used to investigate the asymptotic behaviour of these graphs. For N, n → ∞ in such a way that 1 < n/N < ζ(τ), where ζ(τ) is the value of the Riemann zeta function at the point τ, we obtain limit distributions of the maximum degree and the number of vertices of a given degree.
© de Gruyter 2008
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- Random graphs of Internet type and the generalised allocation scheme
- Limit distributions of the number of vectors satisfying a linear relation
- On design of circuits of logarithmic depth for inversion in finite fields
- The order of communication complexity of PIR-protocols
- On start states of an automaton model of lung in pure environment
- A solution of the power conjugacy problem for words in the Coxeter groups of extra large type
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- A lower bound for the affinity level for almost all Boolean functions
Articles in the same Issue
- Random graphs of Internet type and the generalised allocation scheme
- Limit distributions of the number of vectors satisfying a linear relation
- On design of circuits of logarithmic depth for inversion in finite fields
- The order of communication complexity of PIR-protocols
- On start states of an automaton model of lung in pure environment
- A solution of the power conjugacy problem for words in the Coxeter groups of extra large type
- Asymptotic bounds for the affinity level for almost all Boolean functions
- A lower bound for the affinity level for almost all Boolean functions
